Approximation not falls within the expected range

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Zhuoying Lin
Zhuoying Lin 2017-11-14
编辑： Walter Roberson 2024-12-4
Here's my script:
n=1;
while abs(pi-sum(4./((2*(1:n)-1).*(-1).^((1:n)+1))))>0.001
n=n+1;
end
fprintf('The approximation using Leibniz''s formula falls within 0,001 of pi when it equals to\n')
fprintf('%.9f with n equls %d\n\n',sum(4./((2*(1:n)-1).*(-1).^((1:n)+1))),n)
end
As shown, I try to make the result falls within 0.001 of pi, however, I get n=1000 an approximation equals 3.140592654.
My friend gets n=2002, so is mine wrong?
Thank you!

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回答（1 个）

ag
ag 2024-12-4
Hi Zhuoying,
I kindly suggest you to refer the following MathWorks file exchange page, which demonstrates implementation of the Leibniz formula: Approximation of Pi - https://www.mathworks.com/matlabcentral/fileexchange/102659-approximation-of-pi-leibniz-formula
You can find the code on the "Functions" tab.
Hope this helps!

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